New Testament texts indicate Matthew, Mark and Luke were contemporaries, and the authors of “The New Jerome Biblical Commentary” provide dates (and other evidence) to verify this. St. Peter refers to “Mark, my son” in his first letter (see 1 Pt 5:13), and tradition identifies Peter as the source of information Mark includes in his Gospel account. Scholars date his account to about A.D. 65.
Tradition identifies Matthew as the tax collector Jesus invites to be an apostle (see Mt 9:9), and scholars believe he relied on Mark’s account when recording his Gospel. The same experts also suggest someone else might have used Matthew’s name and written the account about A.D. 90.
No one seems to question Luke’s authorship of the Gospel account bearing his name, nor do scholars find reason to doubt he was, as he remarks in the Acts of the Apostles, an early companion of St. Paul. Scholars believe his Gospel account was written around A.D. 80-85.
The synoptic Evangelists certainly knew individuals who knew one another intimately, and Mark and Luke may have lived in Rome for a period at the same time. However, we have no information — and no tradition — to suggest they knew one another.